# gst: chimera states on m-directed hypergraphs.

<< Chimera states are synchronization patterns in which coherent and incoherent regions coexist in systems of identical oscillators. This elusive phenomenon has attracted a lot of interest and has been widely studied, revealing several types of chimeras. Most cases involve reciprocal pairwise couplings, where each oscillator exerts and receives the same interaction, modeled via networks. >>️

<< However, real-world systems often have non-reciprocal, non-pairwise (many-body) interactions. From previous studies, it is known that chimera states are more elusive in the presence of non-reciprocal pairwise interactions, while easier to be found when the latter are reciprocal and higher-order (many-body). >>️

<< In this work, (AA) investigate the emergence of chimera states on non-reciprocal higher-order structures, called m-directed hypergraphs, and (They) show that, not only the higher-order topology allows the emergence of chimera states despite the non-reciprocal coupling, but also that chimera states can emerge because of the directionality. >>️

<< Finally, (AA) compare the latter results with the one resulting from non-reciprocal pairwise interactions: their elusiveness confirms that the observed phenomenon is thus due to the presence of higher-order interactions. The nature of phase chimeras has been further validated through phase reduction theory. >>️

Rommel Tchinda Djeudjo, Timoteo Carletti, et al. Chimera states on m-directed hypergraphs. arXiv: 2506.12511v1 [nlin.PS]. Jun 14, 2025. 

https://arxiv.org/abs/2506.12511

Also: chimera, network, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chimera, networks, non-reciprocal pairwise interactions, non-reciprocal higher-order structures, m-directed hypergraphs.

# gst: nonstationary critical phenomena: expanding the critical point.

<< A prototypical model of symmetry-broken active matter -- biased quorum-sensing active particles (bQSAPs) -- is used to extend notions of dynamic critical phenomena to the paradigmatic setting of driven transport, where characteristic behaviours are nonstationary and involve persistent fluxes. >>

<< To do so, (AA) construct an effective field theory with a single order-parameter -- a nonstationary analogue of active Model B -- that reflects the fact that different properties of bQSAPs can only be interpreted in terms of passive thermodynamics in appropriately chosen inertial frames. This codifies the movement of phase boundaries due to nonequilibrium fluxes between coexisting bulk phases in terms of a difference in effective chemical potentials and therefore an 'unequal' tangent construction on a bulk free energy density. >>

<< The result is both an anomalous form of coarsening and, more generally, an exotic phase structure; binodals are permitted to cross spinodal lines so that criticality is no longer constrained to a single point. >>

<< Instead, criticality, with exponents that are seemingly unchanged from symmetric QSAPs, is shown to exist along a line that marks the entry to an otherwise forbidden region of phase space. The interior of this region is not critical in the conventional sense, but retains certain features of criticality, which (AA) term pseudo-critical. >>

<< Whilst an inability to satisfy a Ginzburg criterion implies that fluctuations remain relevant at macroscopic scales, finite-wavenumber fluctuations grow at finite rates and exhibit non-trivial dispersion relations. The interplay between the growth of fluctuations and the speed at which they move relative to the bulk results in distinct regimes of micro- and meso-phase separation. >>

Richard E. Spinney, Richard G. Morris. Nonstationary critical phenomena: expanding the critical point. Phys. Rev. E 111, 064129. Jun 23, 2025.

https://journals.aps.org/pre/abstract/10.1103/hx6n-9qsk

arXiv: 2412.15627v2 [cond-mat.stat-mech]. Jun 25, 2025. 

https://arxiv.org/abs/2412.15627

Also: particle, disorder & fluctuations, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particles, active particles, disorder & fluctuations, criticality, pseudo-criticality, transitions.

# gst: turbulence spreading and anomalous diffusion on combs.

<< This (AA) paper presents a simple model for such processes as chaos spreading or turbulence spillover into stable regions. In this simple model the essential transport occurs via inelastic resonant interactions of waves on a lattice. The process is shown to result universally in a subdiffusive spreading of the wave field. The dispersion of this spreading process is found to depend exclusively on the type of the interaction process (three- or four-wave), but not on a particular underlying instability. The asymptotic transport equations for field spreading are derived with the aid of a specific geometric construction in the form of a comb. >>

<< The results can be summarized by stating that the asymptotic spreading proceeds as a continuous-time random walk (CTRW) and corresponds to a kinetic description in terms of fractional-derivative equations. The fractional indexes pertaining to these equations are obtained exactly using the comb model. >>

<< A special case of the above theory is a situation in which two waves with oppositely directed wave vectors couple together to form a bound state with zero momentum. This situation is considered separately and associated with the self-organization of wave-like turbulence into banded flows or staircases. >>

<< Overall, (AA) find that turbulence spreading and staircasing could be described based on the same mathematical formalism, using the Hamiltonian of inelastic wave-wave interactions and a mapping procedure into the comb space. Theoretically, the comb approach is regarded as a substitute for a more common description based on quasilinear theory. Some implications of the present theory for the fusion plasma studies are discussed and a comparison with the available observational and numerical evidence is given. >>

Alexander V. Milovanov, Alexander Iomin, Jens Juul Rasmussen. Turbulence spreading and anomalous diffusion on combs. Phys. Rev. E 111, 064217 – Published 24 June, 2025

https://journals.aps.org/pre/abstract/10.1103/cmf5-sf8x#d93038b1-6671-419d-be1e-219e5bf78523

Also: waves, turbulence, walk, self-assembly, instability, chaos, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, turbulence, walk, self-assembly, instability, chaos, comb model, inelastic resonant interactions, inelastic wave-wave interactions, continuous-time random walk, self-organization of wave-like turbulence, Lévy flights, Lévy walks

# game: Parrondo's paradox in space-inhomogeneous quantum walks.

<< The term Parrondo's paradox refers to the apparently paradoxical effect whereby two or more dynamics in which a given quantity decreases are combined in such a way that the same quantity increases in the resulting dynamics. >>

AA << show that Parrondo's paradox can occur not only in the case of homogeneous but also in space-inhomogeneous one-dimensional discrete-time quantum walks. >>

<< Moreover, (They) demonstrate that for such quantum walks Parrondo's paradox can affect the time evolution of quantum entanglement differently than it does in the case of homogeneous ones. >>

Zbigniew Walczak, Jarosław H. Bauer. Parrondo's paradox in space-inhomogeneous quantum walks. Phys. Rev. E 111, 064218. Jun 25, 2025.

https://journals.aps.org/pre/abstract/10.1103/k6nn-n6c4

Also: Parrondo, game, in https://www.inkgmr.net/kwrds.html 

Keywords: Parrondo, games

# gst: topological phase transition under infinite randomness

<< In clean and weakly disordered systems, topological and trivial phases having a finite bulk energy gap can transit to each other via a quantum critical point. In presence of strong disorder, both the nature of the phases and the associated criticality can fundamentally change. >>

Here AA << investigate topological properties of a strongly disordered fermionic chain where the bond couplings are drawn from normal probability distributions which are defined by characteristic standard deviations. Using numerical strong disorder renormalization group methods along with analytical techniques, (AA) show that the competition between fluctuation scales renders both the trivial and topological phases gapless with Griffiths like rare regions. >>

<< Moreover, the transition between these phases is solely governed by the fluctuation scales, rather than the means, rendering the critical behavior to be determined by an infinite randomness fixed point with an irrational central charge. (AA) work points to a host of novel topological phases and atypical topological phase transitions which can be realized in systems under strong disorder. >>

Saikat Mondal, Adhip Agarwala. Topological Phase Transition under Infinite Randomness. arXiv: 2506.19913v1 [cond-mat.dis-nn]. Jun 24, 2025.

https://arxiv.org/abs/2506.19913

Also: order, disorder, disorder & fluctuations, random, transition, forms of power, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, order, disorder, disorder & fluctuations, randomness, criticality, transitions, forms of power

FonT: who knows if during some master's courses on the organization and evolution of social enclosures, held by the legendary "Frattocchie School" ( https://it.m.wikipedia.org/wiki/Scuola_delle_Frattocchie ) during the early 80s (but also early 90s) some bizarre theoretician advanced the imaginative, up in the air, absolutely unfounded hypothesis (here it is emphasized: absolutely), about the possibility of an immediate cracking of a social structure due to the action of idiots (?) disguised as idiots until the complete, universal, ontheback breakthrough anzicheforse?

# gst: predicting the response of structurally altered and asymmetrical networks.

AA << investigate how the response of coupled dynamical systems is modified due to a structural alteration of the interaction. The majority of the literature focuses on additive perturbations and symmetrical interaction networks. >>

<< Here, (AA) consider the challenging problem of multiplicative perturbations and asymmetrical interaction coupling. (They) introduce a framework to approximate the averaged response at each network node for general structural perturbations, including non-normal and asymmetrical ones. >>

Their << findings indicate that both the asymmetry and non-normality of the structural perturbation impact the global and local responses at different orders in time. (AA) propose a set of matrices to identify the nodes whose response is affected the most by the structural alteration. >>

Melvyn Tyloo. Predicting the response of structurally altered and asymmetrical networks. arXiv: 2506.14609v1 [cond-mat.dis-nn]. Jun 17, 2025.

https://arxiv.org/abs/2506.14609

Also: network, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, multiplicative perturbations, asymmetrical interaction coupling

# gst: random interaction in active matter models; critical changes in Vicsek's scenario.

<< Randomness plays a key role in the order transition of active matter but has not yet been explicitly considered in pairwise interaction connection. In this paper, (AA) introduce the perception rate 𝑃 into the Vicsek model as the probability of the interaction connections and model the connections as superposition states. (They) show that with increasing 𝑃, the polar order number undergoes an order transition and then saturation. >>

<< The order transition is a first-order phase transition with band formation, and the effect of 𝑃 is different from density. The change of the order number is linked with the interaction structure. The order transition, order saturation, and phase separation correspond to different critical changes in the local interaction number. >>

<< The global interaction structure is further analyzed as a network. The decrease of 𝑃 is comparable to random edge removal, under which the network experiences modal transitions near the critical points of the order number, and the network exhibits surprising robustness.  (AA) results suggest that random interaction can be a new important factor in active matter models, with potential applications in robotic swarms and social activities. >>

Ruizhi Jin, Kejun Dong. Role of random interaction connection in the order transition of active matter based on the Vicsek model. Phys. Rev. E 111, 064122. Jun 17, 2025.

https://journals.aps.org/pre/abstract/10.1103/9rdd-tbn7

arXiv: 2501.10669v1 [cond-mat.soft]. Jan 18, 2025. 

https://arxiv.org/abs/2501.10669

Also: network, random, perception, transition, swarm, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, active matter, network, randomness, perception, criticality, transitions, swarm.